According to Globalchange.umich.edu, the human population growth curve is currently following an exponential curve or a "J-shape".
Human Populations via kwout
For the last 50 years, world population multiplied more rapidly than ever before, and more rapidly than it is projected to grow in the future. In 1950, the world had 2.5 billion people; and in 2005, the world had 6.5 billion people. By 2050, this number could rise to more than 9 billion (see chart "World Population Growth, 1950-2050").
Anthropologists believe the human species dates back at least 3 million years. For most of our history, these distant ancestors lived a precarious existence as hunters and gatherers. This way of life kept their total numbers small, probably less than 10 million. However, as agriculture was introduced, communities evolved that could support more people.
World population expanded to about 300 million by A.D. 1 and continued to grow at a moderate rate. But after the start of the Industrial Revolution in the 18th century living standards rose and widespread famines and epidemics diminished in some regions. Population growth accelerated. The population climbed to about 760 million in 1750 and reached 1 billion around 1800.
View U.S. and World Population at Census.gov.
Of interest, watch human population grow from 1 CE to present and see projected growth in under six minutes at Populationeducation.org.